Modeling the relationships between tree crown and DBH and tree height for eight pine species in China

doi:10.13466/j.cnki.lczyyj.2025.02.015

Abstract

Abstract:

Crown condition may be viewed as the determinant of the growth vigor of trees,and the two key characteristic factors are crown width and crown length.There is a close relationship between crown width(CW)or crown length(CL)and diameter at breast height(DBH)and/or height of trees,but most of the studies in this area were based on local data,and few studies were carried out based on large-scale data.Using the measurement data of 1 354 representative sample trees of eight pine species collected throughout the whole country of China,the relationships between CW or CL and DBH and/or tree height were studied by using nonlinear regression estimation,mixed model and dummy variable model methods.The results showed:1)CW was positively correlated with DBH and negatively correlated with ratio of tree height to DBH;the linear model based on DBH alone can explain 80% of the variation of CW,but adding tree height or ratio of tree height to DBH has little effect on the prediction accuracy of CW.2)The ratio of CW to DBH of young trees was relatively high,but it decreased rapidly with the increase of DBH,and began to stabilize when the DBH reached 10 cm or more.3)CL had a nonlinear correlation with DBH and height,with R² of ≥0.75;and the ratio of CL to height was positively related to DBH and negatively related to tree height.4)The average ratios of CL to height in all diameter classes had little variation,and decreased with the increase of DBH below 10 cm,but increased slowly when the DBH exceeded 10 cm;and in the same diameter class,the ratio of CL to height decreased with the increase of tree height.There are some differences among the eight pine species in the above relationships.The correlation between CW,CL,DBH and tree height is of practical significance to further study forest competition and guide scientific forest management.

Key words: crown width, ratio of crown width to stem diameter, crown length, ratio of crown length to tree height, mixed model, dummy variable model

CLC Number:

S711

ZOU Wentao, ZENG Weisheng, WEN Xuexiang. Modeling the relationships between tree crown and DBH and tree height for eight pine species in China[J]. Forest and Grassland Resources Research, 2025, (2): 141-150.

Figures/Tables 8

Tab.1

Fig.1

Tab.2

Tab.3

Tab.4

The estimates of random parameters in mixed models and specific parameters in dummy variable models and the evaluation indexes for the tree species

模型	模型编号	树种	随机或特定参数	树种效应	评价指标
模型	模型编号	树种	$a 1 i$ 或 $b 3 i$	$b 1 i$ 或 $c 3 i$	R²	SEE/m	TRE/%	ASE/%	MPE/%	MPSE/%
混合模型	(1)	马尾松	0.422 9	-0.016 0	0.810	1.09	0.27	-0.70	2.80	19.62
		油松	-0.117 1	-0.002 9	0.813	0.98	-0.22	0.81	4.13	19.41
		云南松	0.210 5	-0.013 5	0.803	1.18	0.25	-1.35	4.42	19.96
		思茅松	-0.249 9	0.055 0	0.910	1.03	-0.09	-1.23	3.34	14.14
		高山松	-0.355 6	-0.013 3	0.834	1.06	-0.69	-1.21	4.58	21.14
		黄山松	-0.131 0	-0.024 6	0.829	0.98	-0.38	-0.57	4.31	23.22
		樟子松	0.475 4	0.011 9	0.773	1.38	0.69	1.11	4.49	21.94
		湿地松	-0.255 2	0.003 4	0.896	0.73	-0.40	-0.76	3.03	14.39
	(3)	马尾松	0.042 2	-0.066 1	0.757	1.71	1.55	3.37	3.16	20.90
		油松	-0.220 2	0.326 4	0.844	1.32	1.18	3.43	3.57	18.82
		云南松	-0.197 7	0.260 2	0.813	1.77	0.45	1.56	4.67	18.74
		思茅松	0.149 9	-0.178 5	0.867	1.32	-0.57	-1.91	3.40	14.85
		高山松	0.329 0	-0.405 7	0.766	1.65	1.21	0.37	4.21	19.28
		黄山松	-0.003 1	-0.058 5	0.785	1.40	-5.52	-9.07	4.76	21.66
		樟子松	0.019 7	-0.015 5	0.660	2.29	-0.48	-2.01	6.09	26.08
		湿地松	-0.119 8	0.137 7	0.834	1.12	-0.29	1.62	3.36	18.12
	(1)
哑变量模型		马尾松	0.470 1	-0.018 0	0.810	1.09	0.00	-1.30	2.80	19.63
		油松	-0.130 0	-0.002 5	0.813	0.98	0.00	1.28	4.13	19.54
		云南松	0.260 3	-0.015 8	0.803	1.18	0.00	-2.01	4.42	20.08
		思茅松	-0.325 9	0.059 4	0.910	1.02	0.00	0.01	3.33	14.06
		高山松	-0.399 7	-0.012 2	0.834	1.06	0.00	0.31	4.58	21.71
		黄山松	-0.127 6	-0.025 6	0.829	0.98	0.00	-0.20	4.31	23.28
		樟子松	0.552 8	0.009 3	0.773	1.38	0.00	-0.14	4.49	21.70
		湿地松	-0.300 0	0.005 4	0.896	0.73	0.00	0.41	3.03	14.42
	(3)	湿地松	-0.300 0	0.005 4	0.896	0.73	0.00	0.41	3.03	14.42
		马尾松	0.048 1	-0.073 8	0.757	1.71	1.63	3.46	3.16	20.92
		油松	-0.262 8	0.383 7	0.844	1.32	0.98	4.12	3.57	19.24
		云南松	-0.207 7	0.272 4	0.813	1.77	0.61	2.07	4.67	18.96
		思茅松	0.184 8	-0.220 7	0.867	1.32	-0.94	-2.53	3.40	14.92
		高山松	0.356 7	-0.440 3	0.767	1.65	0.77	-0.18	4.21	19.32
		黄山松	-0.007 7	-0.057 5	0.786	1.40	-4.29	-7.91	4.75	21.63
		樟子松	0.028 8	-0.026 4	0.660	2.29	-0.62	-2.15	6.09	26.05
		湿地松	-0.140 2	0.162 6	0.834	1.12	0.19	2.48	3.36	18.50

Tab.4

Fig.2

Fig.3

Fig.4

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树种	胸径/cm			树高/m			冠幅/m			冠长/m
树种	最小值	最大值	平均值± 标准差	最小值	最大值	平均值± 标准差	最小值	最大值	平均值± 标准差	最小值	最大值	平均值± 标准差
马尾松	1.2	47.2	16.5±11.9	1.6	30.3	12.1±7.2	0.60	11.73	4.43±2.50	0.7	17.5	6.14±3.46
油松	1.2	32.9	15.3± 9.9	1.6	20.1	9.4±4.8	0.75	10.42	3.85±2.25	0.9	13.3	5.99±3.33
云南松	1.8	47.1	16.7±12.4	1.8	33.3	10.7±6.9	0.75	12.59	4.31±2.64	0.8	26.1	6.10±4.07
思茅松	1.6	46.2	16.7±12.1	1.9	26.4	11.4±6.8	0.75	14.15	4.96±3.39	1.1	17.2	6.26±3.60
高山松	1.5	53.0	16.9±12.1	1.9	31.3	10.2±6.3	0.15	11.75	3.74±2.59	0.9	15.4	6.32±3.39
黄山松	1.2	41.8	16.3±11.8	1.6	24.1	10.6±6.0	0.45	10.05	3.67±2.35	0.3	15.6	4.74±3.01
樟子松	1.5	38.7	16.4±11.7	1.9	27.7	10.9±6.3	0.78	13.44	4.95±2.87	0.9	19.1	6.07±3.91
湿地松	1.2	33.9	15.5± 9.8	1.6	20.0	9.8±4.8	0.85	9.00	3.85±2.21	1.0	12.0	5.32±2.66
合计	1.2	53.0	16.3±11.6	1.6	33.3	10.8±6.4	0.15	14.15	4.24±2.65	0.3	26.1	5.90±3.49

模型	模型参数					评价指标
模型	a_i	b_i	c_i	d_i		R²		SEE/m		TRE/%		ASE/%		MPE/%		MPSE/%
(1)	0.896	0.205			0.800		1.18		0.00		-0.53		1.49		21.59
(2)	1.202	0.200	-0.285		0.801		1.18		0.00		-0.31		1.49		21.57
(3)	0.551	0.477	0.410		0.756		1.73		0.02		-0.13		1.56		21.21
(4)	-1.129	-0.011 3	0.045 0	0.770	0.750		1.75		1.56		5.95		1.58		24.27
(5)	1.229	0.754			0.764		3.09		-0.80		-3.52		1.53		23.11

模型	模型编号	固定或全局参数			评价指标
模型	模型编号	a_i	b_i	c_i	R²	SEE/m	TRE/%	ASE/%	MPE/%	MPSE/%
混合模型	(1)	0.852 8	0.206 8	/	0.840	1.07	0.00	-0.51	1.34	19.26
	(3)	0.468 4^*	0.464 4	0.477 5	0.787	1.62	0.00	0.09	1.47	19.92
	(5)	1.277 0^*	0.735 6	/	0.787	2.97	-0.94	-3.93	1.46	22.47
哑变量模型	(1)	0.846 7	0.207 1	/	0.840	1.07	0.00	-0.33	1.34	19.32
	(3)	0.467 5^*	0.459 1	0.484 9	0.787	1.62	0.08	0.32	1.46	20.05
	(5)	1.280 8^*	0.734 2	/	0.787	2.95	-0.92	-3.91	1.46	22.47